Invalidity of Preissmann Scheme for Transcritical Flow

The Preissmann scheme, often referred to as the four-point scheme, is a bidiagonal implicit finite-difference method for solution of the de St. Venant equations. It is unconditionally stable and extremely robust, and thus is one of the most widely used methods in free-surface one-dimensional subcritical numerical modeling. The purpose of this technical note is to discuss the limitations of Preissmann scheme when applied to transcritical flow. In particular, the analysis presented shows that the Preissmann scheme cannot be used to simulate transcritical flow using the through (shock capturing) method.